Eur. Phys. J. D 61, 709-715 (2011)
https://doi.org/10.1140/epjd/e2010-10342-5

Soliton solutions and interactions of the Zakharov-Kuznetsov equation in the electron-positron-ion plasmas

¹ School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing, 100876, China
² State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China
³ Key Laboratory of Information Photonics and Optical Communications (BUPT), Ministry of Education, P.O. Box 128, Beijing University of Posts and Telecommunications, Beijing, 100876, China

Corresponding author: ^a tian.bupt@yahoo.com.cn

Received: 9 June 2010
Revised: 11 September 2010
Published online: 14 January 2011

Abstract

Analytically investigated in this paper is the Zakharov-Kuznetsov equation which describes the propagation of the electrostatic excitations in the electron-positron-ion plasmas. By means of the Hirota method and symbolic computation, the bilinear form for the Zakharov-Kuznetsov equation is derived, and then the N-soliton solution is constructed. Parametric analysis is carried out in order to illustrate that the soliton amplitude and width are affected by the phase velocity, ion-to-electron density ratio, rotation frequency and cyclotron frequency. Propagation characteristics and interaction behaviors of the solitons are also discussed through the graphical analysis. The effects of the nonlinearity A, dispersion B and disturbed wave velocity C on the amplitude and velocity of the solitons are derived. First, the amplitude is proportional to the nonlinearity A and inversely proportional to dispersion B. Second, the velocity increases as the dispersion B increases. Third, the velocity increases as the disturbed wave velocity C (4B > C) increases; the velocity decreases as the disturbed wave velocity C (4B < C) increases.